What is the largest four-digit number whose digits add up to 16?
Answer: For the number to be as large as possible, the leftmost digit should be as large as possible. Therefore, the thousandth digit should be $9$. The other three digits would have to add up to $16-9=7$. The leftmost digit is now the hundredth digit, which should be the largest number possible, $7$. Therefore, the largest four-digit number possible is $\boxed{9700}$.